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On approximation and interpolation of entire functions with index-pair $(p,q)$

1994; Autonomous University of Barcelona; Volume: 38; Linguagem: Inglês

10.5565/publmat_38294_01

2014-4350

Harvir Singh Kasana, Devendra Kumar,

Mathematical functions and polynomials

In this paper we have studied the Chebyshev and interpolation errors for functions in C(E) , the normed algebra of analytic functions on-a compact set E of positive transfinite diameter .The (p, q)-order and generalized (p, q )-type have been characterized in terms of ,these approximation errors .Finally, we have obtained a saturation theorem for f E C(E) which can be extended to an entire function of (p, q) -order 0 or 1 and for entire functions of minimal generalized (p, q )-type . Introductio nLet E be a compact set in complex plane and 1' (n) = {U, . . ., ~nn } be a system of (n + 1) points of the set E such that n H Inj -'nk 1 and q (j)Wn)}--fi Ir i -Ink l , °Ç jÇkÇn k= q j = o,l , . .., n .Again, let n(n) --{7ni, 7]n2, . . . ,?inri } be the system of (n + 1) points in E such that rz) ) and q °(n( n) ) á(j ) (n(n) ) for j = 1, 2, . . ., n .